equal, proportional and Neyman allocation should be used.

Question 2 A youth development organisation wishes to estimate the proportion of secondary schools in the Western Cape that offer online classes. They decide to stratify by school ownership (state vs. private). Stratum population sizes are displayed below, along with the results of a pilot survey conducted with 50 state schools and 10 private schools. Stratum School Ownership State Stratum Population Size 1200 Pilot Proportion Estimate 0.35 1 Private 2 800 0.73 a) Determine the proportion of the sample to be allocated to each stratum under (1) equal allocation: (11) proportional allocation: (1) Neyman allocation. b) Suppose the overall sample size is 500. Determine the subsample size in each of the strata under each of the three allocation methods. c) Estimate the variance of the proportion estimator under each of the three allocation methods, as well as under SRS. Which method appears to be best? d) Suppose that a sample of size 300 is drawn under Neyman allocation. The sample proportions in the two strata are respectively 0.24 and 0.71. Determine (1) the overall proportion estimate, (tt) an improved estimate of the variance of the proportion estimator, and (iii) a 95% confidence interval for the population proportion. Question 2 A youth development organisation wishes to estimate the proportion of secondary schools in the Western Cape that offer online classes. They decide to stratify by school ownership (state vs. private). Stratum population sizes are displayed below, along with the results of a pilot survey conducted with 50 state schools and 10 private schools. Stratum School Ownership State Stratum Population Size 1200 Pilot Proportion Estimate 0.35 1 Private 2 800 0.73 a) Determine the proportion of the sample to be allocated to each stratum under (1) equal allocation: (11) proportional allocation: (1) Neyman allocation. b) Suppose the overall sample size is 500. Determine the subsample size in each of the strata under each of the three allocation methods. c) Estimate the variance of the proportion estimator under each of the three allocation methods, as well as under SRS. Which method appears to be best? d) Suppose that a sample of size 300 is drawn under Neyman allocation. The sample proportions in the two strata are respectively 0.24 and 0.71. Determine (1) the overall proportion estimate, (tt) an improved estimate of the variance of the proportion estimator, and (iii) a 95% confidence interval for the population proportion